“…For each isotope, denoted as the jth group, and individual, denoted as the ith group, we computed the difference (D) between the treatment and control sample as: D ji = X treatment − X control , where X represents δ 13 C, δ 15 N or δ 34 S and where D ji ~N(μ j , σ 2 ), denoting that D is drawn from a normal distribution with mean μ j and variance σ 2 . We used a semi-informative prior for μ (μ j ~N(0,1)) with prior information coming from Lemons et al (2012) and Bopp et al (2022), who found that differences between treatment and control groups were between 0 and 1‰ for whole blood. We chose a semi-informative prior, rather than an uninformative prior, as the incorporation of prior information into Bayesian models increases the precision of parameter estimations (Banner et al 2020).…”